Learning objective


1) A meter stick moves past you at great speed. If you measure the the length of the moving meter stick to be 0.760 m. -- for example, relative to a meter stick that is at rest relative to you -- what is the speed that the meter stick is moving relative to you?

2) In the year 2010 a spacecraft flies over the moon Station III at a speed of 0.800c. A scientist on the moon measures the length of the spacecraft to be 160m. The spacecraft later lands on the moon, and the same scientist measures the length of the now stationary spacecraft. What value does he get?

3) An unstable particle is created in the upper atmosphere from a cosmic ray and travels straight down towards the surface of the earth with a speed of 0.99860c relative to the earth. A scientist on the surface of earth measures that the particle was created at an altitude of 60.0 Km.

a) As measured by the scientist, how much time does it take for the particle to travel to the surface of the earth?

b) Use the length contraction formula to calculate the distance from when the particle is created to the surface of the earth, in the particle's frame?

c) In the praticle's frame, how long does it take for it to travel from its origin to the surface of the earth? Calculate this time both by the time dialation formula and also from the distace calculated in part b) Do the two results agree?

4) A muon created 20.0 Km. above the earth's surface (as measured in earth's frame) is moving with a speed relative to the earth of 0.9954c. The lifetime of the muon, as measured in its own frame, is 2.2 x 10^-6 seconds. In the frame of the muon, the earth is moving towards the muon with a speed of 0.9954c.

a) In the muon's frame, what is ist height above the earth?

b) In the muon's frame, how much closer does the earth get during its lifetime? What fraction of this is the muon's height as measured from the muon's frame?

c) In the earth's frame, what is the lifetime of the muon? In the earth's frame, how far does the muon travel during its lifetime? What fraction of this is the muon's height as measured from the earth's frame?